Computationally-Efficient Linear Periodically Time-Variant Digital PLL Modeling Using Conversion Matrices and Uncorrelated Upsampling
arxiv(2024)
摘要
This paper introduces a conversion matrix method for linear periodically
time-variant (LPTV) digital phase-locked loop (DPLL) phase noise modeling that
offers precise and computationally efficient results to enable rapid design
iteration and optimization. Unlike many previous studies, which either assume
linear time-invariance (LTI) and therefore overlook phase noise aliasing
effects, or solve LPTV systems with noise folding and multiple sampling rate
conversions that heightens modeling and computational complexity, the proposed
conversion matrix method allows the designer to represent the LPTV systems
using intuitive LTI-like transfer functions with excellent accuracy.
Additionally, computational efficiency is improved through the uncorrelated
upsampling method, which eliminates the need to consider beat frequency of
noise sources with different sampling rates. The proposed algorithm is applied
to modeling a DPLL with time-varying proportional loop gain, and the modeling
accuracy is validated with Simulink transient simulations.
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